Suspicious behavior of TUnuran::SampleMulti

[DingXuefeng]

• Checked for duplicates

Describe the bug

It seems that to sample a N-dimensional vector, we need to call this method N times.

See log file:

for (int j = 0; j < 20000; j++) {
    hzmodel.Sample(&flux_real[0]);
    if(j<10)
    std::cout<<j<<" "<<flux_real[0]<<" "<<flux_real[1]<<" "<<flux_real[2]<<std::endl;

output

1 5.73992 4.99711 4.88
2 5.73992 4.99711 5.26624
3 5.72944 4.99459 5.25179
4 5.34123 4.99459 5.25179
5 5.34123 4.96792 5.25179
6 5.34123 4.96792 5.2696
7 5.26477 4.99232 5.52042
8 5.59451 4.99232 5.52042
9 5.59451 5.04631 5.52042

Expected behavior

By calling SampleMulti, all components should be randomized.

To Reproduce

try ROOT tutorial

Setup

tested on
ubuntu 20.04 + ROOT v6.26.00 (wget)
ubuntu 20.04 + ROOT v6.24.06 (wget)
MacOS 10.15 + ROOT v6.26.00 (brew)

Additional context

N/A

[DingXuefeng]

It seems deeper problems exists. In my study, I need to sample a 3D multi-variate gaussian distribution. For comparison, I set correlation to zero, so that I can simply sample three independent variables. The results using unuran and the one using three indepent variables are incompatible, even with above mentioned dirty fix.

Currently I switch to alternative methods, yet it might be useful to understand what is the problem.

I think some unit test and integration test should be implemented.

[lmoneta]

The problem is that the default method Unuran uses for multi-dimensional distribution (hitro) is based on Markov-Chain MC so it is expected to observe this behaviour if you look at the single events, instead, you should use at the generated obtained distribution. See for example https://search.r-project.org/CRAN/refmans/Runuran/html/hitro.new.html
If you switch unuran (in the TUnuran::Init) to use the method vnrou then it will be fine when looking at the single events generated.
Before closing this issue, I think we need to improve the documentation in TUnuran for this.